Athanasios D. Karageorgos

On the solution of higher order linear homogeneous complex σ–α descriptor matrix differential systems of Apostol–Kolodner type

Abstract In this paper, the solution of higher order linear homogeneous complex σ–α descriptor matrix differential systems of Apostol–Kolodner type is investigated by considering pairs of complex matrices with symmetric and skew symmetric structural properties. The results are very general, and they derive under congruence of the Thompson canonical form. The regularity (or singularity) of a matrix pencil pre-determines the number of sub-systems respectively. The special structure of these kinds of systems derives from applications in engineering, physical sciences and economics. A numerical example illustrates the main findings of the paper.

Discretizing LTI Descriptor (Regular) Differential Input Systems with Consistent Initial Conditions

A technique for discretizing efficiently the solution of a Linear descriptor (regular) differential input system with consistent initial conditions, and Time-Invariant coefficients (LTI) is introduced and fully discussed. Additionally, an upper bound for the error that derives from the procedure of discretization is also provided. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena.

Power series solutions for linear higher order rectangular differential matrix control systems

This paper is concerned with the solution of linear higher order rectangular differential matrix systems which are appeared in many applications of optimal and filtering control theory. The classical power series method is employed to obtain the analytic solution of linear higher order rectangular (singular) differential matrix equations. In the present paper, the authors provide some preliminary results for solving linear singular matrix systems with the power series approach.

The dynamic response of homogeneous LTI descriptor differential systems under perturbations of the right matrix coefficients

This paper is concerned with the dynamic response of a general class of linear time invariant differential systems, the right parameter of which undergoes step perturbations. We solve both systems using the complex Weierstrass canonical form (powerful tool of matrix pencil theory). After that, we calculate and compare the relationship between the two solutions. This comparison is of considerable importance in numerical analysis since it has a direct bearing upon the accuracy of any particular method used to construct the solution of the base system. A numerical example is also provided.

Perturbation Theory for a Homogeneous Descriptor Regular Differential System

Abstract This paper is concerned with the dynamic response of a general class of linear systems, the right parameter of which undergoes step perturbations. We solve both systems using the Weierstrass Canonical form (powerful tool of matrix pencil theory). After that, we calculate and compare the relationship between the two solutions. This comparison is of considerable importance in numerical analysis since it has a direct bearing upon the accuracy of any particular method used to construct the solution of the base system.

Simulate the State Changing of a Descriptor System in (Almost) Zero Time Using the Normal Probability Distribution

In number of control applications, the ability of manipulate the state vector from the input is more than vital. Thus, in the present paper, we develop analytically a methodology for the state changing of a linear control descriptor differential system based also on a linear combination of Dirac δ-function and its derivatives. Using linear algebra techniques and the generalized inverse theory, the input’s coefficients are determined. In our practical numerical application, the Dirac distribution is approximated by the normal probability distribution.

THE DRAZIN INVERSE THROUGH THE MATRIX PENCIL APPROACH AND ITS APPLICATION TO THE STUDY OF GENERALIZED LINEAR SYSTEMS WITH RECTANGULAR OR SQUARE COEFFICIENT MATRICES

In several applications, e.g., in control and systems modeling theory, Drazin in- verses and matrix pencil methods for the studyof generalized (descriptor) linear sy stems are used extensively. In this paper, a relation between the Drazin inverse and the Kronecker canonical form of rectangular pencils is derived and fullyinvestigated. Moreover, the relation between the Drazin inverse and the Weierstrass canonical form is revisited byproviding a more algorithmic approach. Finally, the Weierstrass canonical form for a pencil through the core-nilpotent decomposition method is defined.

Linear Time Invariant Homogeneous Matrix Descriptor (Singular) Discrete-Time Systems with Non Consistent Initial Conditions

Several applications in mechanics, in engineering, as well as, in financial issues, have been benefited by the use of digital computers. Thus, in the literature of system and control theory, the discrete-time systems gained a special merit. In this paper, we discuss the solution properties of a very interesting class of descriptor systems. So, we provide with the solution of linear time invariant homogeneous matrix descriptor (singular) discrete-time systems with non-consistent initial conditions. The lack of consistency to the initial conditions makes the problem more general and too far challenging. Consequently, using the properties of z-transform, the solution is fully discussed and provided.

Solution Properties of Linear Descriptor (Singular) Matrix Differential Systems of Higher Order with (Non-) Consistent Initial Conditions

In some interesting applications in control and system theory, linear descriptor (singular) matrix differential equations of higher order with time-invariant coefficients and (non-) consistent initial conditions have been used. In this paper, we provide a study for the solution properties of a more general class of the Apostol-Kolodner-type equations with consistent and nonconsistent initial conditions.

Symmetric/skew-symmetric homogeneous matrix descriptor (regular) differential systems with consistent initial conditions

This paper introduces the results of Thompsons canonical form under congruence for pairs of complex matrices with symmetric and skew symmetric structural properties to the solution of higher order linear matrix homogeneous differential systems. Under this approach, the main equation is divided into five sub-systems whose solutions are derived. Note that the regularity or singularity of matrix pencil predetermines the number of sub-systems. The special properties of such systems may be appeared in engineering and even in some financial models.